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Communication and Randomness Lower Bounds for Secure Computation

Deepesh Data, Vinod M. Prabhakaran, Manoj M. Prabhakaran
2016 IEEE Transactions on Information Theory  
In this work, we employ information theoretic techniques to obtain lower bounds on the amount of communication and randomness required for secure MPC.  ...  We derive lower bounds for both the perfect security case (i.e., zero-error and no leakage of information) and asymptotic security (where the probability of error and information leakage vanish as block-length  ...  The optimal protocol in Figure 11 , which builds on Körner and Marton's [50] scheme, that we used to show a gap between the rate regions of perfectly and asymptotically secure computations in Section  ... 
doi:10.1109/tit.2016.2568207 fatcat:lml5gnuvkna2nfcni7fv6ypuwy

On the Communication Complexity of Secure Computation [chapter]

Deepesh Data, Manoj M. Prabhakaran, Vinod M. Prabhakaran
2014 Lecture Notes in Computer Science  
We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.  ...  party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case.  ...  Secondly, we show that our lower bounds for communication complexity also yield lower bounds on the amount of randomness needed in secure computation protocols.  ... 
doi:10.1007/978-3-662-44381-1_12 fatcat:zr2xvjjqcvepdmndfnpx4bmrsu

On the Communication Complexity of Secure Computation [article]

Deepesh Data, Vinod M. Prabhakaran, Manoj M. Prabhakaran
2014 arXiv   pre-print
We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.  ...  3-party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case.  ...  So, whenever X and Y are independent, the lower bounds on communication for secure sampling imply lower bounds for secure computation. Correlated Multi-Secret Sharing Schemes.  ... 
arXiv:1311.7584v2 fatcat:ksgnrmbq7zeu3ndj5v63bshcma

More Communication Lower Bounds for Information-Theoretic MPC [article]

Ivan Damgård, Boyang Li, Nikolaj I. Schwartzbach
2021 IACR Cryptology ePrint Archive  
We prove two classes of lower bounds on the communication complexity of information-theoretically secure multiparty computation.  ...  The first lower bound applies to perfect passive secure multiparty computation, in the standard model with n = 2t + 1 parties of which t are corrupted.  ...  Lower bounds for arbitrary functions In this section we prove a lower bound on the communication complexity for perfect passive secure multiparty computation.  ... 
dblp:journals/iacr/DamgardLS21 fatcat:3ujn2dgu35futn3izvm2idptq4

A Quantitative Approach to Reductions in Secure Computation [chapter]

Amos Beimel, Tal Malkin
2004 Lecture Notes in Computer Science  
We explore the hierarchy for randomized protocols as well, giving upper and lower bounds, and comparing it to the deterministic hierarchy.  ...  It is known that all functions can be computed securely in the information theoretic setting, given access to a black box for some complete function such as AND.  ...  We thank Yuval Ishai for helpful discussions and Enav Weinreb for helpful remarks on earlier versions of this paper.  ... 
doi:10.1007/978-3-540-24638-1_14 fatcat:khnh525o6vhrzfyg5nkceqg4fe

Communication Lower Bounds for Perfect Maliciously Secure MPC [article]

Ivan Damgård, Nikolaj I. Schwartzbach
2020 IACR Cryptology ePrint Archive  
We prove a lower bound on the communication complexity of perfect maliciously secure multiparty computation, in the standard model with n = 3t + 1 parties of which t are corrupted.  ...  We show that for any n and all large enough g ∈ N there exists a Boolean circuit C with g gates, where any perfectly secure protocol implementing C must communicate Ω(ng) bits.  ...  To show our results, we start from a lower bound for the communication complexity of a specific function for the case of 4 parties and 1 maliciously corrupt player.  ... 
dblp:journals/iacr/DamgardS20 fatcat:glqimx5avbhtvmqr7y3rrtt74y

Some contributions of the study of abstract communication complexity to other areas of computer science

Juraj Hromkovič
1999 ACM Computing Surveys  
, and for the development of some kind of secure communication protocols in the practice  ...  Here, we concentrate on the applications of communication complexity for the study of several fundamental computing models, for the comparison of the power of deterministic, and probabilistic computations  ...  One of the perspectives is to extend the applications for proving lower bounds for multilective and/or non-oblivious computing models.  ... 
doi:10.1145/333580.333587 fatcat:uh26qnj3ozhv5e35qccvdszuje

Non-Local Box Complexity and Secure Function Evaluation

Marc Kaplan, Iordanis Kerenidis, Sophie Laplante, Jérémie Roland, Marc Herbstritt
2009 Foundations of Software Technology and Theoretical Computer Science  
We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case.  ...  Oblivious Transfer calls Alice and Bob need in order to securely compute a function f .  ...  Acknowledgements We would like to thank Troy Lee and Falk Unger for pointing out the deterministic protocol for Disjointness.  ... 
doi:10.4230/lipics.fsttcs.2009.2322 dblp:conf/fsttcs/KaplanKLR09 fatcat:54js7gjnsbem3hmjzh6efvqcsq

Page 6758 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
Summary: “Problems of secure communication and computation have been studied extensively in network models.  ...  Goldreich, Gold- wasser, and Linial, Franklin and Yung, and Franklin and Wright have initiated the study of secure communication and secure computation in multi-recipient (broadcast) models.  ... 

Placing Conditional Disclosure of Secrets in the Communication Complexity Universe

Benny Applebaum, Prashant Nalini Vasudevan
2021 Journal of Cryptology  
Finally, our results show that proving explicit super-logarithmic lower-bounds for imperfect CDS protocols is a necessary step towards proving explicit lower-bounds against the class AM, or even AM ∩ coAM  ...  security.  ...  The logarithmic lower-bounds for CDS follow from Theorem 1 (and the fact that the corresponding predicates have linear randomized one-way communication complexity.)  ... 
doi:10.1007/s00145-021-09376-1 fatcat:a6kbdqw64vh4hhs4ra3pt4d2la

On the Communication Required for Unconditionally Secure Multiplication [chapter]

Ivan Damgård, Jesper Buus Nielsen, Antigoni Polychroniadou, Michael Raskin
2016 Lecture Notes in Computer Science  
Thus, while information-theoretic secure protocols are very efficient in terms of computational work, they (seem to) require more communication and more rounds than computationally secure protocols.  ...  Many information-theoretic secure protocols are known for general secure multi-party computation, in the honest majority setting, and in the dishonest majority setting with preprocessing.  ...  Lower bounds for secure function evaluation in the preprocessing model.  ... 
doi:10.1007/978-3-662-53008-5_16 fatcat:p7r2bk46ojfipdvppkr6mqmziu

On the Cryptographic Complexity of the Worst Functions [chapter]

Amos Beimel, Yuval Ishai, Ranjit Kumaresan, Eyal Kushilevitz
2014 Lecture Notes in Computer Science  
A similar result holds for securely sampling a uniform pair of outputs from a set S ⊆ [N ]×[N ]. -Correlated randomness complexity of secure two-party computation.  ...  Every function f : [N ] × [N ] → {0, 1} can be securely evaluated using 2 O( √ log N) bits of correlated randomness. -Communication complexity of private simultaneous messages.  ...  Winkler and Wulschlegger [56] prove an Ω(log N ) lower bound on the correlated randomness complexity of secure two-party computation.  ... 
doi:10.1007/978-3-642-54242-8_14 fatcat:q3ccfhvn5jea5fnlvvqoydjhau

Two Party Distribution Testing: Communication and Security [article]

Alexandr Andoni, Tal Malkin, Negev Shekel Nosatzki
2018 arXiv   pre-print
These lower bounds are of independent interest as these are the first 2-party communication lower bounds for testing problems. 3) Security: we define secure distribution testing and argue that it must  ...  The gain is polynomially better than what one obtains by adapting standard algorithms. 2) Lower bounds: we prove tightness of our protocols for the closeness testing, and for the independence testing when  ...  Work supported in part by Simons Foundation (#491119), NSF grants CCF-1617955 and CCF-1740833.  ... 
arXiv:1811.04065v1 fatcat:ex5aroidovcypil5jodjav4744

Optimally Efficient Secure Scalar Product with Applications in Cloud Computing

Babak Siabi, Mehdi Berenjkoub, Willy Susilo
2019 IEEE Access  
To show the optimality of this SSP protocol, information theoretic lower bounds on the amount of communicated data in a secure two-party computation in the preprocessing model are derived.  ...  Secure computation of scalar product is of considerable importance due to its central role in many practical computation scenarios with privacy and security requirements.  ...  In Section III, we focus on efficiency of secure two-party computations and derive lower bounds on communications complexity of such computations.  ... 
doi:10.1109/access.2019.2908230 fatcat:iafuld6uujcd7cslthwdevkpo4

Optimal Lower Bound for Differentially Private Multi-party Aggregation [chapter]

T-H. Hubert Chan, Elaine Shi, Dawn Song
2012 Lecture Notes in Computer Science  
Both of our lower-bounds, for the general setting and the client-to-server communication model, are strictly stronger than those of Beimel, Nissim and Omri, since we remove the assumption on the number  ...  We prove a tight lower bound for the private distributed summation problem.  ...  To see why the lower bound is tight for the general multi-party setting, we combine standard techniques of secure function evaluation [CK93] and distributed randomness [SCR + 11] and show in Section  ... 
doi:10.1007/978-3-642-33090-2_25 fatcat:d2nxboaryzhmbh4rlqorkwlzoa
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